Given i a, b e Z, b # 0, , consider thefollowing affirmations regarding Euclides's algorithm:9,r €Nbq +r, r < |b|а1)There aresuch that9,r E Za = bq +r, r < b2)There aresuch thatWhat can we say?A) Both true.B) 1 is true and 2 is false.C) 1 is false and 2 is true.D) Bothfalse.

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Answered: Given a,b e Z, b + 0, , consider…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(5) (Extra credit, 5 points) Show that 102n-1 +1 is divisible by 11 (namely, 102n−1 +1 = 11 ·an, where a₁ = 1 and an+1 = 100an 9 for all natural numbers n = 1, 2, ...). [Hint: Show that 102n+1+1=100 (102n−1 + 1) - 99.]
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Given a,b e Z, b + 0, , consider thefollowing affirmations regarding Euclides's algorithm: 1)There are 9," EN, such that a - bq +r, r < [b| 2)There are 9," EZ such that a = bq +r, r < b What can we say? A) Both true. B) 1 is true and 2 is false. C) 1 is false and 2 is true. D) Bothfalse.